Bounded‐influence rank estimation in the linear model

We introduce and study a class of rank‐based estimators for the linear model. The estimate may be roughly described as being calculated in the same manner as a generalized M‐estimate, but with the residual being replaced by a function of its signed rank. The influence function can thus be bounded, both as a function of the residual and as a function of the carriers. Subject to such a bound, the efficiency at a particular model distribution can be optimized by appropriate choices of rank scores and carrier weights. Such choices are given, with respect to a variety of optimality criteria. We compare our estimates with several others, in a Monte Carlo study and on a real data set from the literature.